d. 1. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of gL
forever. If gL < WACC, what is a formula for the present value of expected free
cash flows when discounted at the WACC?
Answer:
d. 2. If the most recent free cash flow is expected to grow at a constant rate of gL
forever (and gL < WACC), what is a formula for the present value of expected
free cash flows when discounted at the WACC?
Answer:
e. 1. Use B&M’s data and the free cash flow valuation model to answer the following
questions. What is its estimated value of operations?
Answer:
e. 2. What is its estimated total corporate value? (This is the entity value.)
Answer: Total corporate value = Vop + Short-term investments.
e. 3. What is its estimated intrinsic value of equity?
Answer: Intrinsic value of equity = Total value- Debt – Pref.
 
L
1
op gWACC
FCF
V
 
L
L0
op
gWACC
)g1(FCF
V
 
 
420
05.011.0
)05.01(24
V
gWACC
)g1(FCF
V
op
L
L0
op
f. 1. You have just learned that B&M has undertaken a major expansion that will
change its expected free cash flows to −$10 million in 1 year, $20 million in 2
years, and $35 million in 3 years. After 3 years, free cash flow will grow at a rate
of 5%. No new debt or preferred stock were added, the investment was financed
by equity from the owners. Assume the WACC is unchanged at 11% and that
there are still 10 million shares of stock outstanding. What is its horizon value
(i.e., its value of operations at year three)? What is its current value of
operations (i.e., at time zero)?
Answer:
Year 0 1 2 3 4 5 … t
0 WACC = 11% 1 2 3 gL = 5% 4 N
| | | | | |
-10 20 35
$ -9.009
f. 2. What is its value of equity on a price per share basis?
Answer:
Value of operations $480.67
g. If B&M undertakes the expansion, what percent of B&M’s value of operations
at Year 0 is due to cash flows from Years 4 and beyond? Hint: use the horizon
value at t = 3 to help answer this question.
Answer: First, calculate the present value of the horizon value. Then divide the present value
of the horizon value by the Year 0 value of operations. This will show what percent of
value is due to cash flows occurring 4 or more years in the future.
Percent of value due to cash flows from Year 4 and beyond:
05.011.0
h. Based on your answer to the previous question, what are two reasons why
managers often emphasize short-term earnings?
Answer: 1. Changes in quarterly earnings can signal changes future in cash flows. This would
i. Your employer also is considering the acquistion of Hatfield Medical Supplies.
You have gathered the following data regarding Hatfield, with all dollars
reported in millions: (1) most recent sales of $2,000; (2) most recent total net
operating capital, OpCap = $1,120; (3) most recent operating profitability ratio,
OP = NOPAT/Sales = 4.5%; and (4) most recent capital requirement ratio, CR =
OpCap/Sales = 56%. You estimate that the growth rate in sales from Year 0 to
Year 1 will be 10%, from Year 1 to Year 2 will be 8%, from Year 2 to Year 3 will
be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the
long-term growth rate beyond Year 4 will be 5%. Assume the operating
profitability and capital requirement ratios will not change. Use this information
to forecast Hatfield’s sales, net operating profit after taxes (NOPAT), OpCap,
free cash flow, and return on invested capital (ROIC) for Years 1 through 4. Also
estimate the annual growth in free cash flow for Years 2 through 4. The weighted
average cost of capital (WACC) is 9%. How does the ROIC in Year 4 compare
with the WACC?
Answer:
The operating items are forecast as follows: Sales1 = $2,000(1+0.10) = $2,200;
Scenario:
No Change
Actual Forecast
0 1 2 3 4
Sales
$2,00
0
$2,20
0
$2,37
6 $2,495 $2,620
NOPAT $99 $107 $112 $117.879
$1,23
$1,397.08
The ROIC4 is 8% and the WACC is 9%. This means that ROIC < WACC/(1+gL) at the
j. What is the horizon value at Year 4? What is the value of operations at Year 0?
How does the value of operations compare with the current total net operating
capital?
Answer:
HV 4=FCF4(1+gL)
(WACC−gL)=$48.025(1+0.05)
(0.09−0.05)=$1,260.65
Value of Operations:
Present value of HV $893.08
Notice that the value of operations at Year 4 (i.e., the horizon value, HV4) is
Also, at Year 0, the most recent total net operating capital, OpCap0 = $1,120. Note
that the value of operations at Year 0 is $958, and this is less than the OpCap0. Thus,
the low ROIC relative to the WACC causes the value of operations to be less than the
total net operating capital.
k. What are value drivers? What happens to the ROIC and current value of
operations if expected growth increases by 1 percentage point relative to the
original growth rates (including the long-term growth rate)? What can explain
this? Hint: Use Scenario Manager.
Answer: Value drivers are the inputs to the FCF valuation model that managers are able to
influence: sales growth rates, operating profitability, capital requirements, and cost of
capital.
Scenario No Change Improve Growth
g0,1 10% 11%
g1,2 8% 9%
Higher growth causes Vop,0 to fall. ROIC must be greater than WACC/(1+WACC) for
growth to add value.
l. Assume growth rates are at their original levels. What happens to the ROIC and
current value of operations if the operating profitability ratio increases to 5.5%?
Now assume growth rates and operating profitability ratios are at their original
levels. What happens to the ROIC and current value of operations if the capital
requirement ratio decreases to 51%? Assume growth rates are at their original
levels. What is the impact of simultaneous improvements in operating
profitability and capital requirements? What is the impact of simultaneous
improvements in the growth rates, operating profitability, and capital
requirements? Hint: Use Scenario Manager.
Answer: .
Scenario No Change Improve OP
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
The improvement in operating profitability increases the ROIC, which increases the value of
operations.
Scenario No Change Improve CR
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
The improvement in capital requirements increases the ROIC, which increases the value of
operations.
Scenario No Change Improve OP and CR
g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
The improvements in operating profitability and capital requirements increased the ROIC, so
growth now adds substantial value.
Scenario No Change Improve All
g0,1 10% 11%
g1,2 8% 9%
g2,3 5% 6%
The improvements in operating profitability increased the ROIC, so growth now adds substantial
value.
m. What insight does the free cash flow valuation model give provide us about
possible reasons for market volatility? Hint: Look at the value of operations for
the combinations of ROIC and gL in the previous questions.
Answer: .
ROIC
Small changes in ROIC and growth cause large changes in value. Similarly, small